Heat the olive oil in a large skillet over medium-high heat.
Add the diced onion and sauté until soft, about 4–5 minutes; add the minced garlic during the last minute and cook until fragrant.
Stir in the chicken broth, uncooked orzo, undrained canned diced tomatoes, Italian seasoning, kosher salt, and crushed red pepper flakes; bring the mixture to a boil.
Reduce heat to a simmer, cover the skillet, and cook for 12–15 minutes, stirring occasionally, until most of the liquid is absorbed and the orzo is tender.
Stir in the shredded rotisserie chicken and chopped spinach during the last 3 minutes of cooking until the spinach wilts and the chicken is heated through.
Remove from heat, sprinkle with grated Parmesan, and serve immediately.